REGULARITY OF SEMIGROUPS IN TERMS OF HYBRID IDEALS AND HYBRID BI-IDEALS

Abstract

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals and hybrid bi-ideals. We also characterize the left and right simple and the completely regular semigroups utilizing hybrid ideals and hybrid bi-ideals. We show that a semigroup S is left simple if and only if it is hybrid left simple. We also prove that if a semigroup S is intra-regular, then for each hybrid ideal (j) over tilde (mu) of S, we have (j) over tilde (mu)(r(1)r(2)) = (j) over tilde (mu) (r(2)r(1)) for all r(1), r(2) is an element of S.